Large cardinal chart of Ramsey-like cardinals

A while ago Joel Hamkins suggested that I copy cat this post of Norman’s: Chart of large cardinals near high-jump with my own large cardinal chart. So here is the large cardinal chart of Ramsey-like cardinals and their relationship to other large cardinal notions. The Ramsey-like cardinals: $\alpha$-iterable cardinals ($1\leq\alpha\leq\omega_1$), strongly Ramsey cardinals, super Ramsey cardinals, and superlatively Ramsey cardinals were introduced by myself and/or Philip Welch. All relevant definitions are here.

@AsafKaragila I should have done a better job stating my question clearly. I wanted to know precisely what Yair answered: whether there are models where $\text{cf}(j(\kappa))$ is smaller than the size of $j(\kappa)$. Your interpretation of the question is very interesting as well, but I think much harder to answer.